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RoseWind [281]
2 years ago
12

Sam the scout is going on a camp out with his boy-scout troop. There are large tents that sleep 6 boys and small tents that slee

p 4 boys. The ratio of large tents to small tents is 8 to 5. There are exactly enough tents to sleep 816 boys. How many tents of each size are there?
Mathematics
1 answer:
natita [175]2 years ago
5 0

Answer:

There are 96 large tents and 60 small tents

Step-by-step explanation:

Here, we want to calculate the number of tents of each sizes there

Let the number of 6-boys tent be s and the number of 4-boys tent be f

6s + 4f = 816 ••••••(i)

Ratio of large to small ( ratio of s to f)

8:5 = s/f

8/5 = s/f

8f = 5s

f = 5s/8 ••••(ii)

Substitute ii into i

6s + 4(5s/8) = 816

6s + 5s/2 = 816

Multiply through by 2

12s + 5s = 1,632

17s = 1632

s = 1632/17

s = 96

f = 5s/8

f = (5 * 96)/8 = 60

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When you see the symbol "△", this denotes a triangle. Now combine the symbol with the letters FGH, this becomes △FGH, meaning a triangle FGH, with F, G, and H as the three points.

Now, the symbol "∠" means angle and "m∠" means the measure of an angle. So m∠F means the angle at the point F, m∠G means the angle at the point G, and m∠H means the angle at the point H. (I'll attach a diagram of this triangle).

Now we have to determine m∠H, which is the angle at point H. To do that, we have to find the value of x. To do that, we have to use one of the laws of a triangle, which is:

The sum of angles in a triangle = 180°. This means when we add all the angles in a triangle, it sums up to 180°. Let's do that.

\angle F + \angle G + \angle H = 180\textdegree \\\angle F = (5x - 6)\textdegree, \angle G = (3x + 16)\textdegree, \angle H = (x + 8)\textdegree \\(5x - 6) + (3x + 16) + (x + 8) = 180\\5x + 3x + x - 6 + 16 + 8 = 180\\9x + 18 = 180\\9x = 180 - 18\\9x = 162\\x = 18\textdegree

Now that we have found the value of x as 18°, we can substitute its value to determine the angle H.

m\angle H = (x + 8), x = 18\\m\angle H = 18 + 8\\m\angle H = 26\textdegree

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